For $g\isin\Z$ , let $\bar{g}\isin\Z_{37}$ denote the residue class of g modulo 37. Consider the group U 37 = { $\bar{g}\isin\Z_{37}:1\le g\le37$ with gcd(g, 37) = 1} with respect to multiplication modulo 37. Then which one of the following is FALSE?

Question

For $g\isin\Z$ , let  $\bar{g}\isin\Z_{37}$  denote the residue class of g modulo 37. Consider the group U 37 = { $\bar{g}\isin\Z_{37}:1\le g\le37$  with gcd(g, 37) = 1} with respect to multiplication modulo 37. Then which one of the following is FALSE?

cdquestions Admin · Accepted Answer

The correct option is (B): The order of the element $\overline{10}$  in U 37 is 36.

Answer

The set ${\bar g \isin U_{37}: \bar g = (\bar g)^{-1}}$ contains exactly 2 elements.

Answer

The order of the element $\overline{10}$ in U₃₇ is 36.

Answer

There is exactly one group homomorphism from U₃₇ to ($\Z$, +).

Answer

There is exactly one group homomorphism from U₃₇ to ($\mathbb{Q}$,+).

For \(g\isin\Z\), let \(\bar{g}\isin\Z_{37}\) denote the residue class of g modulo 37. Consider the group U₃₇ = {\(\bar{g}\isin\Z_{37}:1\le g\le37\) with gcd(g, 37) = 1} with respect to multiplication modulo 37. Then which one of the following is FALSE?

The Correct Option is B

Solution and Explanation

Top Questions on Groups

Questions Asked in IIT JAM MA exam

For \(g\isin\Z\), let \(\bar{g}\isin\Z_{37}\) denote the residue class of g modulo 37. Consider the group U37 = {\(\bar{g}\isin\Z_{37}:1\le g\le37\) with gcd(g, 37) = 1} with respect to multiplication modulo 37. Then which one of the following is FALSE?

The Correct Option is B

Solution and Explanation

Top Questions on Groups

Questions Asked in IIT JAM MA exam

For \(g\isin\Z\), let \(\bar{g}\isin\Z_{37}\) denote the residue class of g modulo 37. Consider the group U₃₇ = {\(\bar{g}\isin\Z_{37}:1\le g\le37\) with gcd(g, 37) = 1} with respect to multiplication modulo 37. Then which one of the following is FALSE?